Abstract: The talk introduces a conjecture on the first exit time of fractional Brownian motion: the upper-tail probability for a fractional Brownian motion to first exit a positive-valued barrier over time […]
Abstract: A proper coloring of a graph is an assignment of colors from \( \{1, 2, \ldots, k\} \) to each node of a graph such that no two nodes […]
Abstract: The three-dimensional incompressible Euler equations describe the motion of an ideal fluid, yet the mechanisms that govern the possible loss of regularity of smooth solutions remain only partially understood. […]
Abstract: Existing tools for explaining complex models and systems are associational rather than causal and do not provide mechanistic understanding. We propose a new notion called counterfactual explainability for causal […]
Abstract: We present a new approach for deriving structure-preserving numerical discretizations of Fokker-Planck equations by establishing a connection between the Fokker-Planck equation and its semi-discrete master equation at the level […]
Abstract: The Shapley value is a ubiquitous framework for attribution in machine learning, encompassing feature importance, data valuation, and causal inference. However, its exact computation is generally intractable, necessitating efficient […]
Abstract: This talk presents a regularity criterion for the three-dimensional Navier–Stokes equations based on finitely many observations of the flow. Motivated by data assimilation, we study a nudging algorithm that […]
Abstract: In this talk, we will describe a well/ill-posedness result for the 2D incompressible Euler equations. We investigate solutions in a setting logarithmically smoother than previously done, in a hope […]
Abstract: We study the optimization of Steklov eigenvalues with respect to a boundary density function ρ on a bounded Lipschitz domain. We investigate the minimization and maximization of a Steklov […]
Abstract: Turbulence influences our lives in a multitude of ways, ranging from the mundane (when we stir milk into our coffee) to the spectacular (the formation of galaxies). It is […]
Abstract: I will introduce In-Context Operator Networks (ICON), a framework in which a single neural network learns solution operators for differential equations directly from a few prompted input-output examples at inference time, without any weight updates. ICON acts as a few-shot learner across forward and inverse problems for ODEs, PDEs, and mean-field control. I will […]
Abstract: Consider n independent, biased coins, each with a known probability of heads. Presented with an ordering of these coins, flip (i.e., toss) each coin once, in that order, until we have observed both a head and a tail, or flipped all coins. The Unanimous Vote problem asks us to find the ordering that minimizes […]
